In this paper, the averaging principle for Conformable fractional stochastic differential equations with Lévy noise was investigated. Firstly, the averaging principle of the classical Itô type Conformable fractional stochastic differential equations is given. Secondly, the averaging principle with Lévy noise is also given. Different from the approach of integration by parts or decomposing integral interval to deal with the estimation of integral involving singular kernel in the existing literature, we use a new method to estimate the error of the solution between the averaged stochastic equation and the conformable fractional stochastic differential equations, and overcome the integral involving singular kernel. Finally, a simulation example is given to verify the correctness of the theoretical analysis.

In this paper, we study the averaging principle for Caputo type fractional stochastic differential equations with Lévy noise. Firstly, the estimate on higher moments for the solution is given. Secondly, under some suitable assumptions, we show that the solutions of original equations can be approximated by the solutions of averaged equations in the sense of pth moment and convergence in probability by Hölder inequality. Finally, a simulation example is given to verify the theoretical results.